"Insert into orbit" is indeed absolutely correct, as can be seen from these search results.
However, the word insert is being used there in a rather technical context. Unless someone is already familiar with the jargon of spaceflight or orbital mechanics, the word insert might sound a little awkward at first exposure.
Many words are like this: they have secondary or idiomatic meanings that may sound awkward or maybe even incorrect – at least until you've heard it used in that particular context a few times. Besides inserting a satellite into orbit, other examples might include:
- a large aircraft that taxis to the runway
- a politician who dances around a question
- a cold wind that bites into your skin
- when you bump into your friend at the grocery store
- deciding to eat chicken vice fish
- the rake who disrupts the formal dinner party
- an algorithm designed to keep data coherent
I would guess that the textbook where the O.P. found this question is rather advanced, and deliberately uses words in a scientific, technical, or otherwise specialized context, so as to expose the reader to the broader uses of some words.